Traditional Versus Non-Traditional Reinsurance in a Dynamic Setting

We consider a stochastic risk reserve process whose risk exposure can be controlled dynamically by applying proportional reinsurance and by issuing CAT Bonds. The CAT Bond payments are only partly correlated with the insurers losses. The aim is to minimize the probability of ruin. Using a two-dimensional diffusion approximation we obtain a controlled diffusion problem which can be solved explicitly with the help of the HJB equation. We present some numerical results and discuss to which extend the proportional reinsurance can be replaced by issuing CAT Bonds.

Keywords: Optimal Control, Hamilton-Jacobi-Bellman Equation, Diffusion Approximation, Proportional Reinsurance, Catastrophe Bonds